AirlineDog / capacitated-team-orienteering-problem

A simple heuristic algorithm combined with local search to solve a specific instance

capacitated-team-orienteering-problem

A local search algorithm algorithm for the capacitated team orienteering problem.

In the capacitated team orienteering problem, start and end depots are specified along with other locations which have associated demands, service times and profits. Given a fixed amount of time for each of the M vehicles with limited capacity of the team, the goal is to determine M paths from the start point to the end point through a subset of locations in order to maximize the total profit.

Technics used :

• Heuristic algorithm

  • The first step is to design a simple heuristic algorithm that calculates the ratio $\dfrac{distance + service time + demand}{profit}$. The algorithm greedily selects customers form an Restricted Candidate List until all vehicles are full.

• Local search

  • The next step is to find ways to improve the solution created from the heuristic without examining all possible senarios. This is done by implementing local search operators that afect the solution in a way that differs by a little from the previous one.

    Operators :

    1. Relocate

       Relocate is the process where a selected node (target) is moved from its current position in the route to another position (destination).

    2. Two opt

       The idea of 2-opt is to exchange the links between two pairs of subsequent nodes.

    3. Node addition

       The two previous operators are focued on redusing the travel time of the routes. Next step is to try and improve the solution by adding new nodes and subsequently gain more profit.

    4. Destroy and repair

       This operator focuses on destroying a part of the solution and then reconstructing with an other node to differentiate the solution.

Final solution graphical representation: